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On trichotomy of positive singular solutions associated with the Hardy-Sobolev operator. (English. Abridged French version) Zbl 1168.35011
Summary: We present a complete classification of singularities of positive solutions of the equation \(\Delta u + \frac{\mu}{|x|^2}u = h(u)\) in \(\Omega \setminus \{0\}\), where \(\Omega \) is a bounded domain of \(\mathbb R^N\), \(N\geq 3\), \(0\in \Omega \), and \(0<\mu<\frac{(N-2)^2}{4}\). The case \(\mu =0\) with \(h(t)=t^q\), \(q>1\) were treated by Brezis and Véron.

MSC:
35J60 Nonlinear elliptic equations
35A20 Analyticity in context of PDEs
35A08 Fundamental solutions to PDEs
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